The Truth is in the Eye of the Beholder: or Equilibrium in Beliefs and Rational Learning in Games

Games with incomplete information or randomness in the moves of others typically have many decision-theoretically equivalent formulations of the type space. These different formulations correspond to different ways of encoding tha realizations of randomizations in the type of a player. Solution concepts, assumptions or paradoxes in games should be independent of the formulation of the game used. I refer to this axiom as TIGER, for "Type Independence among Games which are equivalently Re-formulated".